Newmak M. H. A.. Stratified systems of logic. Proceedings of the Cambridge Philosophical Society , vol. 39 (1943), pp. 69–83.

The central problem is this: Given a time parameter t and a condition $(t) concerning the times of excitation of the afferent neurons of a net, find a method of constructing the net so that a specified efferent neuron will fire (be in a state of excitation) at time t if and only if the condition <t>(t) is satisfied. If a sufficient time interval is allowed between the firing of the afferent neurons and the firing of the efferent neuron, the required network can always be constructed without difficulty, at least if <t>{t) does not involve quantifiers. This is true because the problem is easily solved for conditions [<I>{1) & $(l) ], [4>(t) & ~^(<) ], and [$(1) v 4>(t) ] if it can be solved for 0(t) and $(t). Conversely the net may be already given and we may seek a condition on the afferent neurons necessary and sufficient for firing of some specified neuron of the net at a time I. This converse problem can be easily solved, the authors show, if the net does not involve neural pathways that return upon themselves. McCulloch and Pitts, however, go further and deal with networks involving such reentrant pathways and also with conditions involving quantifiers, but proper evaluation of this part of their theory is practically impossible because of numerous errors. FREDERIC B. FITCH